# A university found that of its students withdraw without completing the introductory statistics course. Assume that students registered for the course

A university found that of its students withdraw without completing the introductory statistics course. Assume that students registered for the course. a. Compute the probability that or fewer will withdraw (to 4 decimals). b. Compute the probability that exactly will withdraw (to 4 decimals). c. Compute the probability that more than will withdraw (to 4 decimals).
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“A university found that of its students withdraw without completing the introductory statistics course” here percentage is not given. Let us assume that p of its student withdraw without completing in the course.The number of students registered for the course is n$X\sim \text{Bin}\left(n,p\right)$Part (a): Compute the probability that or fewer will withdraw (to 4 decimals)Here let us assume that we have to find the probability that m or fever will withdraw.By the definition of mass function of X is given as:$P\left(X=x\right)=\left(\begin{array}{}n\\ x\end{array}\right)×{p}^{x}×\left(1-p{\right)}^{n-x}$
$P\left(X\le m\right)=\left[P\left(X=0\right)+P\left(X=1\right)+...+P\left(X=m-1\right)\right]$Part (b): Compute the probability that exactly will withdraw (to 4 decimals).Here also the exact number is not given. Now assume that exactly m’ will withdraw.The probability that exactly m’ will withdraw:$P\left(X={m}^{\prime }\right)=\left(\begin{array}{c}n\\ {m}^{\prime }\end{array}\right)×{p}^{x}×\left(1-p{\right)}^{n-m}$Part (c): Compute the probability that more than M will withdraw (to 4 decimals).Assume that the required number is M.The probability that more than M will withdraw:$P\left(X>M\right)=1-P\left(X\le M\right)$